1. |
- Benedicks, Michael, et al.
(författare)
-
Random perturbations and statistical properties of Henon-like maps
- 2006
-
Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 23:5, s. 713-752
-
Tidskriftsartikel (refereegranskat)abstract
- For a large class of non-uniformly hyperbolic diffeomorphisms, we prove stochastic stability under small random noise: the unique stationary probability measure of the Markov chain converges to the Sinai-Ruelle-Bowen measure of the unperturbed attractor when the noise level tends to zero.
|
|
2. |
- Lindgren, Erik, et al.
(författare)
-
On the two-phase membrane problem with coefficients below the Lipschitz threshold
- 2009
-
Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 26:6, s. 2359-2372
-
Tidskriftsartikel (refereegranskat)abstract
- We study the regularity of the two-phase membrane problem, with coefficients below the Lipschitz threshold. For the Lipschitz coefficient case one can apply a monotonicity formula to prove the C-1,C-1-regularity of the solution and that the free boundary is, near the so-called branching points, the union of two C-1-graphs. In our case, the same monotonicity formula does not apply in the same way. In the absence of a monotonicity formula, we use a specific scaling argument combined with the classification of certain global solutions to obtain C-1,C-1-estimates. Then we exploit some stability properties with respect to the coefficients to prove that the free boundary is the union of two Reifenberg vanishing sets near so-called branching points.
|
|
3. |
- Pinchover, Yehuda, et al.
(författare)
-
A Liouville-type theorem for the p-Laplacian with potential term
- 2008
-
Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 25:2, s. 357-368
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p-Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the linear case (p = 2), this condition involves comparison of both the functions and of their gradients.
|
|